why in ques 83, while preparing partners capital a/c hidden goodwill method is used?

No hidden goodwill method is not used in this question. The share of goodwill that Z brings in at the time of his admission is clearly stated in the question. Therefore, hidden goodwill method is not required. 

Hidden goodwill method is used when value of goodwill is not mentioned and it is to be calculated by deducting Net Worth of the business from Capitalised value of the firm.

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